902 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 5, NO. 3, AUGUST 1990

HINIHIZATION OF UNCWTAINTIES IN ANALOG HEASUREKENTS FOR USE IN STATE ESTIMATION

M. M. Adibi, SM, IRD Corporation, Bethesda, Maryland

Abstract: The uncertainty in an analog measurement is a combination of systematic error and random error. The systematic error completely dominates the random error and varies in a recognizable pattern over the range of measurement.

In this paper a range of analog measurements is obtained from a transmission station, spanning peak and light-load conditions. Then the redundancies in measurements are used to formulate several functions relating these measurements with their attending errors. Minimization of these functions has yielded the required correction coefficients which are used to minimize the systematic errors and to evaluate the actual random errors, both of which are required by the state estimation.

The approach developed uses voltage, real and reactive power measurements which generally are available and used by state estimators. Current measurement is limited to a critical line or transformer per substation.

Keywords: Remote Measurement Calibration, Instrument Accuracy, Systematic Error Correction, Random Error Evaluation.

INTRODUCTION

Power system reliability and economy of opera- tion require accurate measurements of current, voltage, real and reactive powers. Typically, several thousands of these measurements are telemetered to the control center for monitoring, control and use in various computer applications.

Each measurement is the final product of a chain of instruments and processes. The chain consists of instrument transformers, transducers, and analog-to-digital convertors linked together with “secondary” wiring at the substation; scaling and conversion procedures at the control center; and telemetering gear and communication equipment in between. These devices, linkages, equipment and procedures all, to a different degree, introduce errors in the measurement streams. The instruments drift and deteriorate with time, temperature and environmental conditions requiring periodic inspection and calibration.

There has been a need for an efficient and economic approach for calibration of the measurements and for identification of defective instruments. The approach described in this paper attempts to meet the industry’s

90 Wbl 235-2 PWRS A paper recornmended and approved by t h e IEEE Power System Engineering Committee of the IEEE Power Engineering Society f o r presentat ion a t the IEEE/PES 1990 Winter Meeting, Atlanta , Georgia, February .4 - 8, 1990. August 2 5 , 1989; made ava i lab le f o r p r in t ing January 5 , 1990.

Manuscript submitted

R. J. Kafka, SM, Potomac Electric Power Co.

Washington, D.C.

need by analyzing the historical analog measurements available at the control center, detecting systematic errors in the measurements, correcting such errors by scale adjustments, and evaluating the actual random errors for use in computer control of power systems.

In Ref. 1, an approach is described which requires the full complement of measurements for each line in a substation, measurements of real and reactive powers around each bus, and measurements of voltages on all lines and bus sections to allow the use of MVA Equality, Bus Summing and kV Equality equations.

The MVA Equality, Bus Summing and kV Equality are described as: the equality between volt- ampere derived from real and reactive powers and volt-ampere obtained from the product of current and voltage in a line, the summation of real and reactive powers around a bus, and the equality of all line voltages which are connected to the same bus, respectively.

The above measurements are made over a significant range of the full scale ratings of the instruments, and quadratic scaling is recommended to avoid errors due to non- linearities of current transformer in current, real and reactive power measurements.

Under such an instrument arrangement, measurement ranges, and scaling procedures, the errors in the above equations are simultaneously minimized for all the lines and bus sections, over practically the full range of measurements, and highly accurate calibration coefficients are determined.

In practice, however, there are a number of limitations and considerations which make the error analysis and measurement calibration more challenging. The redundancy in measurements described in Ref. 1 is not realized. In fact, frequently voltage transformers are shared and interchangeably used by lines and power transformers to cut down the costs, and current measurements are limited to the critical lines in the substation. Moreover, it is impractical to modify the large on-line data base in the existing control system to adopt the preferred quadratic scaling. Also, under normal power system operations, measurements vary by a relatively small fraction of their full ranges.

Often, power system measurements are made with single phase instruments. Under this instrument arrangement it is assumed that the three phase currents and voltages are balanced. However, in many cases, even under normal operating conditions, the three phase measurements are imbalanced, influencing the calibration algorithm.

These limitations necessitate consideration of appropriate data preparation procedures, error analysis techniques, and approximate calibration methodologies.

0885-8950/90/0800-02$01.00 0 1990 IEEE

903

The work described here is an extension of the previous effort reported in & 21. It conforms with the industry's instrumentation and scaling practices where generally currents are not monitored, measurements are made on a single phase, and are linearly scaled.

In this paper, first typical instrument characteristics are briefly described. Then an error analysis is presented indicating various sources of errors in the analog measurements. Next the methodology for approximate calibration of voltage, real and reactive powers of a 500/230 kV transmission station wherein currents are not monitored is described. The final section provides a case study together with a conclusion.

BACKGROUND

Four different instrument arrangements have been studied: the single element which assumes balanced 3-phase volts and amperes, the 2- & 2%-element which assume imbalanced 3-phase with no neutral return, and the 3-element which assumes presence of positive, negative and zero sequence volts and amperes.

Typically, power system volts and amperes are reduced to 115 volts and 0-5 amperes by means of voltage transformers (VT) or coupling capacitor voltage transformers (CCVT) & current transformers (CT), [3].

Volts and amperes thus measured and reduced are then fed into volt (V) , ampere (I) , real power (P) and reactive power (Q) transducers (TR), which produce proportional direct currents (dc). The dc output for I-TR and V- TR is 0-1.0 mA, proportional to 0-5 amperes and to 90 to 130 volts, and is fl.O mA for the f5OOwatts (single-element) P-TR and Q-TR.

A precision resistor of 10 k-ohm is used to produce 0-10 volts dc from the 0-1 mA dc TR outputs, which is then converted to 0-12 bits of binary data equivalent to -2048 to +2047 counts by the analog-to-digital convertors (ADC) in the remote terminal units (RTU) and telemetered to the control center (CC).

At the CC the 12 bits binary data are received and linearly scaled into engineering units representing A, kV, MW and Mvar measured. The CT ratios, VT ratios, CCVT ratios, TR ratings and the precision resistor values are used in the scaling procedure.

The exciting current versus the primary voltage for a typical VT, over the normal operating range of 90 to 110%, is very nearly linear. Therefore, binary data representing voltage measurements can linearly be scaled and converted into engineering units,[3].

The exciting current versus primary current for a typical CT over the operating range of 10 to 100% rated primary current is non- linear. The present practice of linearly scaling currents introduces systematic errors,in a recognizable pattern, in A, MW and Mvar measurements.

The CCVT has a lower cost than VT, and it is extensively used for relaying, indicating, and metering purposes. However, it requires peri- odic calibration to maintain its accuracy,[4].

Field tests on a number of I-, V-, P- and Q- transducers have shown that when these transducers are in good condition, the relationship between their inputs and outputs over 20 to 100 percent of their full range is linear, and can be represented linearly. Gain and zero offset of transducers are adjustable.

The analog-to-digital converters used are typically of moderate speed e.p., 25 microseconds per conversion, encoding 210 volts into ?ll bits data, with measurement accuracy of about +.05%.

The combined time constants of instrument transformers and transducers used for I, V, P and Q measurements are about 50 to 100 ms, while the sampling rates of the RTUs are typically 50 points per second. Also, the I, V, P & Q per line are sequentially scanned resulting in a time skew of about 35 ms which can be considered simultaneous when compared with the variation of signals being scanned.

JCRROR ANALYSIS

The analog measurements contain a certain amount of errors which can be of the following four types:

1- The random errors which primarily depend on the degree of precision of the various instruments in the measurement streams. Generally, they are unbiased and normally distributed. Their standard deviations can only be reduced by selection of a higher class of instruments.

2- The systematic errors which are caused by: the drift and deterioration of instruments with time, temperature and environment; deviations in gains, zero offsets, and non- linearities of instruments in the measurement streams; and the inaccurate modeling and scaling at the control center.

3- The installation errors caused by the use of erroneous instrument transformer ratios, transducer ratings, scaling coefficients, and occasionally, reverse instrument polarities.

4- Intermittent errors which are primarily caused by interference in communication, partial and temporary failures of the telemetering gear.

At Potomac Electric Power Company (PEPCo) an off-line program has been developed which cross checks the high and low scales of real and reactive power metering points with their corresponding instrument transformer ratios, ratio correction factors, and transducer ratings to identify and eliminate the installation errors.

After elimination of the installation errors, the remaining uncertainty in the analog measu- rements will be due to a combination of random errors and systematic errors. Minimization of the combined errors, which is the main thesis of this paper, provides the zero-mean and the actual standard deviation of analog measure- ments required by state estimators.

The accuracies in analog measurements thus obtained would reduce the residuals and allow the state estimators to suppress the

904

intermittent errors real-time data-base of the power systems

and furnish dependable for the computer control [51.

9 . . . m i z w n of Svstematic Er- and Evaluation of Random Errors

A reasonable estimate of the combined error, E,, from the systematic error, E,, and the random error, Er, is provided by the square root of the sum of the squares of E, and Er. The objective is to identify the combined errors, E,, in current, voltage, real and reactive power measurements and reduce the E, to the measurement precision or the random errors, Er [6].

In general, the accuracy classification of instrument transformers used by the industry for analog measurements is ANSI Accuracy Class of 0.6. Accordingly, the specified (not the actual) random uncertainties in instruments, measurements and functions can be estimated per [2], as shown in the following table:

SDecified Random Unce rtainties

Instruments CCVT CT TR ADC + ( % I 0.60 0.93 0.65 0.05

Measurements kV A MW Mvar + ( % I 0.89 1.14 1.29 1.29

Functions MVA(1) MVA(2) (R-1) CE = + ( % ) 1.29 1.44 1.93 2.73/&

where MVA(1) is the square root of the sum of the squares of MW & Mvar measurements, MVA(2) is the product of A & kV measurements, R is the ratio of MVA(1) over MVA(2), E=R-1, CEZ is the function to be minimized, and N is the number of accepted measurements.

Figure 1 is a plot of (R-1) against MVA(1) for a 230kV line. It shows that the deviations (R-1) far exceed the expected +1.93% random error derived from the above instrument specifications. Studies undertaken in several power systems indicate that such a large deviation is due to installation and systematic errors which can be eliminated and minimized [2].

Figure 2 shows the extent of improvement in MVA deviations obtained by using the minimization method of [7]. The deviations (R-1) over an 80-200 MW range of measurements for a 230 kV line are compared before and after minimization of the systematic errors. It can be seen that the combined errors in (R-l), have been reduced from a range of 2% to 6% to about +.5%. This is well within the f1.93% which was determined from the specified precision of the instrument chain measuring (R-1). In other words the calibrated curve very closely approximates m i a s e d and normally d istributed values for (1-R).

CALIBRATION OF KV, 1Iw, h WAR

The simplified one-line diagram of the transmission station investigated is shown in Figure 3. It consists of one 500/230kV auto- transformer two 500kV and three 230kV lines.

0 10 20 30 40 50 60 70 EO 90 100 110

Figure 1 - MVA Deviations vs. MVA(1) MVA(1) = (MW’ + Mvar2)#, MVA(2) = f i * (A * kV) * R = MVA(l)/MVA(2), MVA Deviation = (R - 1) * 100, in %.

6

5

4

3

2

1

t .5

0

- . 5

Figure 2 - MVA Deviations vs. MW, Before and After Calibration

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The kV, MW and Mvar measurements monitored are as indicated.

In the following equations:

VI P & Q represent kV, MW & Mvar measurements and v, p 61 q are their corresponding calibrated values,

t, i & j subscripts refer to the auto- transformer and lines as shown,

a, b & c are the measurements' offset, gain and non-linearity coefficients,

a is the auto-transformer's off-nominal ratio, n is the number of "hourly" readings collected over several days, and k = t, i or j.

Using the "A Equality", i.e., equation (2) below, and several days of readings, the calibration coefficients for the auto- transformer's kV, MW & Mvar measurements are calculated, and consequently, the calibrated values of vt, pt & qt are determined.

The relationship between auto-transformer's measured and calibrated values for each "hourly" scan can be written as:

vt = alt + blt*Vt + clt*Vt2,

pt = a2t + b2t*Pt + c2t*Ptz, and

qt = a3t + b3t*Qt + c3t*Qt2. (1)

To determine the above calibration coefficients the following error function, summed over the n "hourly" data is minimized:

CEz=X[ (Xpi2+Cqi2)~/vi - c~*(ptz+~t~)#/vt]~. (2)

500kV BU

AUTO-TRANSF.

t o V-Tr, P-Tr & Q-Tr

j = l m

e-Iline Diaara Transm ission Station On *

230kV BUS i=v fiaure 3

The intent is to use the auto-transformerfs calibrated values vt, pt & qtr as references to correct the three linefs voltages, real and reactive power measurements.

From the "kV Equality" for each tthourlyll scan we have :

vt = aj + bj*Vj + cj*Vj2, (3)

where, vt is the calibrated kV for the auto- transformer, a b & c * are the kV calibration coeffjicients, and Vj is the kV measurements for line j. The calibration coefficients for the three lines are to be determined by quadratic fitting of vt and Vj for the n "hourly'l data.

From the Bus Summing for each "hourly" scan we have :

Pt + CPj = 0,

pj = aj + bj*Pj + c *P j j -Pt = xaj + Cbj*Pj + XCj*Pj2, ( 4 )

where, pt is the calibrated MW for the auto- transformer, a , b & c' are the MW calibration coefjicienis, and Pj is the MW measurement for line j. The least squares solution of -pt and Pj for the N "hourly" data would produce bjl cj and xaj.

Now supressing the Zaj, i.e., Caj=O, we have:

-pt = 0 + Cbj'*Pj + Xcj'*Pj*, ( 5 )

A second least squares solution of -pt and Pj, would produce bj' and cj'.

NOW; pj = aj + bj*Pj + C.*P i j ( 6 )

and pj' = 0 + bj'*Pj+ cjf*Pj2, (7)

where pi = pjf . Then aj x (bj'-bj)*Pj + (cjf- cj)*Pj2, or

ajf = (bj'-bj)*Pj + (cj'- Cj)*PjZl (8)

where Pj & Pj2 are the average values of Pj & Pj2 for line j, over the N llhourlyll data.

Finally, we have:

pj" = aj' + bj*Pj + c.*P 3 j , (9) ,

where pj" is the calibrated value for Pj.

A similar procedure can be applied to determine the calibration coefficients and corrections of the reactive power flows in the three lines.

The minimization of equation (2) also provides calibration coefficients for Vir ZPi and ZQi which can be applied using the above procedure to calibrate Vi, Pi and Qi.

In summary, by having the current measurements available only in the autotransformer, one is able to calibrate and minimize systematic errors in voltage, real and reactive powers of the three lines as well. The measured and calibrated data then can be used to determine standard deviations for kV, MW & Mvar of every line and the autotransformer.

The "zero-mean" measurements and the "actual" standard deviations thus obtained can be used by state estimator to provide a real-time data-base for real-time contingency checks and for other monitoring and control functions.

A Case Studv

In order to test the above approach, the following experiment was conducted on the 500/230kV Transmission Station (TS) of Fig.3. The TS has the full complement of measurements on the secondary side of the autotransformer and on all the three lines.

From the historical data file, 96 "hourly" readings were obtained for all the

906

measurements, spanning peak and light-load conditions covering two weekdays and a weekend. This provided an adaquate range of measurements.

In order to conform with the present practice of linear scaling the linear version of the Remote Measurement Calibration (RMC) Program of Ref. 1, was used and the calibration coefficients, i.e., gains and zero offsets, were obtained. These calibration coefficients were then used to minimize the systematic errors in all the measurements.

For brevity, Table 1 shows a subset of the 9 6 llhourlyft calibrated MW values. To provide a perfect set for the experiment, the calibrated values in Table 1 were slightly adjusted to reduce the rms errors in Bus Summing over the subset to about 1.0E-14.

Table 2 shows the corresponding simulated measurements. It was derived from the Table 1 data by introducing the following gain and zero offset errors which are the rounded gains and zero off-sets obtained from the above RMC run.

pt = at + bt*Pt = 3 . 5 0 + 0 . 9 7 5 * P t ,

p1 = al + bl*P1 =-1.50 + 1.025*P1,

p2 = a2 + b2*P2 = 1 . 5 0 + 1.015*P2, &

p3 = a3 + b3*P3 =-1.00 + 0.985*P3. (1)

The above gains and zero offset errors resulted in an rms error in Bus Summing of about 10 MW as shown in Table 2.

A multiple regression of -pt from Table 1 on Pl , P2 & P3 of Table 2 , resulted in the following gains and sum of the zero offsets:

bl = 1 . 0 2 5 0 ,

b2 1 . 0 1 5 0 ,

b3 = 0 . 9 8 5 0 , and

Ca j=-1.0. ( 2 )

A second multiple regression of -pt on P I , P2 and P3 of Table 2 , with suppresslon of zero offset, i.e., Caj=O, resulted in:

bl'= 1 . 0 3 1 3 ,

b2'= 1 . 0 1 8 6 ,

b3'= 0 . 9 8 1 3 , and

xaj= 0.0. ( 3 )

Using the average of simulated MW measurements in Table 2 and the above bj & bj' values for lines 1, 2 & 3 , resulted in:

all= - 0 . 7 6 4 6 ,

a2'= 0 . 8 8 6 1 , and

a3'= -1 .1171. ( 4 )

The above gains bj, and zero offsets aj', provide :

p i " =-0.7646 + 1.0250*P1,

p2'l = 0 . 8 8 6 1 + 1.0150*P2, and

p3" =-1.1171 + 0.9850*P3. ( 5 ) These equations were used to calibrate the simulated measurements of Table 2 , and to obtain the corresponding calibrated data in Table 3 .

-224 .01 -70 .88 -231 .84 - 7 4 . 2 1 -256 .97 - 8 9 . 2 1 -278 .74 -99 .73 -241 .39 - 7 8 . 9 5 -323 .60 -109 .91 -309 .86 -109.43 -457 .50 -126 .90 - 4 8 4 . 7 5 -126.88 -326 .50 - 9 3 . 6 1 - 3 9 0 . 4 7 -124 .50 -488 .44 -122 .56 -477 .44 -130 .55 -443 .73 - 1 4 6 . 8 9 -469 .74 -129 .75 -521 .77 -131 .96 -447 .48 -143 .97 -444 .72 -144 .65 -465 .30 -126 .86 -502 .17 -124 .82 -593.24 -165 .85 -504 .81 -144 .57 -475.98 -150 .33 -595 .58 - 1 8 9 . 7 2 -589 .20 -190 .94

1 0 3 . 6 0 1 9 1 . 2 9 1 0 9 . 1 4 1 9 6 . 9 1 1 3 0 . 2 4 215 .94 1 4 6 . 6 3 231 .84 1 1 5 . 0 2 205 .32 1 8 5 . 9 5 247 .57 1 7 8 . 7 2 240 .57 2 7 6 . 5 1 307 .89 2 7 5 . 8 3 335 .80 1 8 1 . 3 1 238 .80 2 4 4 . 7 0 270 .26 273 .87 3 3 7 . 1 3 272 .89 3 3 5 . 1 1 266 .12 3 2 4 . 5 0 264 .92 334 .57 2 9 0 . 8 5 3 6 2 . 8 8 268 .42 3 2 3 . 0 3 2 6 7 . 7 5 3 2 1 . 6 3 3 0 7 . 1 8 2 8 4 . 9 8 2 8 1 . 0 3 345 .96 4 0 3 . 3 7 355 .72 3 3 5 . 1 9 314 .19 2 6 7 . 6 9 358 .62 4 1 9 . 2 8 3 6 6 . 0 3 416 .76 363 .39

0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0 . OQE+OO 0.00E+00 0.00E+00 0.00E4-00 5.683-14 1.14E-13 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 1.14E-13 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 1.14E-13

Table 2- 25 Hourly Simulated Measurements ____________________---_--_--------------- Pt P 1 P2 P3 Pt+SUM(Pi) ______________-__-------------------------

-233 .35 - 6 7 . 6 9 1 0 0 . 5 9 1 9 5 . 2 2 -5.22E+00 -241 .37 -70 .94 1 0 6 . 0 4 200 .93 -5.34E+00 -267 .15 - 8 5 . 5 7 1 2 6 . 8 4 220 .24 -5.643+00 -289 .47 -95 .84 1 4 2 . 9 8 236 .39 -5.94E+00 -251 .17 -75 .56 1 1 1 . 8 4 209 .46 -5.43E+00 -335.49 -105 .77 1 8 1 . 7 2 2 5 2 . 3 5 -7.18E+00 -321 .39 - 1 0 5 . 3 0 1 7 4 . 6 1 245.24 -6.84E+00 -472 .82 -122 .34 270 .95 313 .59 -1.06E+01 -500 .76 -122.33 2 7 0 . 2 8 3 4 1 . 9 3 -1.09E+01 -338 .46 -89 .86 1 7 7 . 1 5 2 4 3 . 4 5 -7 .723+00 -404 .07 -120 .00 2 3 9 . 6 1 2 7 5 . 3 9 -9.07E+00 -504 .56 -118.11 268.35 343 .27 - l . l O E + 0 1 -493 .27 - 1 2 5 . 9 1 2 6 7 . 3 8 341 .22 -1.06E+01 -458 .70 -141 .84 2 6 0 . 7 1 330 .46 -9.38E+00 -485 .38 - 1 2 5 . 1 2 2 5 9 . 5 3 3 4 0 . 6 8 -1.03E+01 -538.74 -127 .27 285 .07 369 .42 -1.15E+01 -462 .54 -139.00 2 6 2 . 9 7 328 .97 -9.60E+00 -459 .72 -139 .66 2 6 2 . 3 1 327 .54 -9.52E+00 -480 .82 -122.30 3 0 1 . 1 6 2 9 0 . 3 3 -1.16E+01 -518 .64 - 1 2 0 . 3 1 275 .40 3 5 2 . 2 5 -1.13E+01 -612.04 -160 .34 3 9 5 . 9 3 3 6 2 . 1 5 -1.43E+01 -521 .35 -139 .58 328 .76 319 .99 -1.22E+01 -491.78 -145 .20 262 .26 3 6 5 . 1 0 -9.623+00 -614 .44 -183 .63 4 1 1 . 6 0 372 .62 -1.39E+01 -607.90 -184 .82 409 .12 369 .94 -1.37E+01

AVG--> -121 .37 2 4 6 . 1 3 301 .93 -9.533+00 RMS--> 9.91E+00

____________________----------------------

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The above approach provides satisfactory results for typical variation of gains and zero offsets, which are between 100+2.5%, and f2.5%, respectively. The larger variations usually indicate defective or out-of-range instruments needing field inspections.

-224.01

-256.97

-241.39 -323.60

-457.50 -484 * 75 -326.50 -390.47

-477.44 -443.73 -469.74 -521.77

-444.72 -465.30 -502.17 -593.24 -504.81

-595.58

-231. 84

-278.74

-309. 86

-488.44

-447.48

-475.98

-589.20

-70.14 -73.48 -88.47

-109. 18 -108.70

-92. a7

-121. a2 -129. 82

-99.00 -78.21

-126.17 -126.15

-123.76

-146.15 -129.02 -131.22 -143.24 -143.92 -126.12

-165.12 -143.83 -149.59 -188. 98 -190.21

-124. 08

102.99

129.63 146.02 114.41 185.34 178.12 275.90 275.22

244.09 273.27

265.51 264.32 290.24

267.14 306.57

402.76

108. 53

180.70

272.28

267.81

280.42

334.58 267. 08 418.67 416.15

191.19 196. ai 215. 83 231.73 205.21 247.46 240.46

335.69

270.15 337.02 335.00 324.39 334.46 362.77 322.92 321.52

307.78

238.69

284. 87 345. a5

314 .oa 358.51

363.28

355.61

365.92

1.893-02 1.893-02 1.893-02 1.893-02 1.893-02 1.893-02 1.893-02 1.893-02 1.893-02 1.893-02 1 .893-02 1.893-02 1.893-02

1.893-02 1.893-02 1. 893-02 1.893-02 1.893-02 1.893-02 1 .893-02 1.893-02 1 .893-02 1.893-02

1.893-02 1.893-02

The rms errors between the perfect set of Table 1 and the calibrated set of Table 3 for each line as a percentage of their full scale ratings, i.e., FSR z 720 MW, are:

L h 2 A ! D L % FSR

#1 0.74 0.103 #2 0.61 0.085 #3 0.11 0.017

It can be seen that the largest rms error in this test is about 0.1% of FSR in Line #I, supporting the validity of the approach.

Tables 2 & 3 show that the combined systematic and random errors in MW Bus Summing has been reduced ,

from rms(.mn) =9.913+00 in MW,

to rms(Cpnn~)=1.89~-02 in MW,

providing 8tzero-mean'9 MW measurements. The reduction in the systematic error and the estimation of standard deviation for each line obtained from tables 2 & 3 are as follows:

Line Systematic Standard Deviations(MW) Number Error in MW Estimated Derived

1 3.87 0.75 9.29 2 4.77 1.31 9.29 3 5.70 0.87 9.29

The reason for the low values of standard deviations is due to the fact that the MW data in Table 2 are simulated Measurements. Experience with actual measurements has shown that the "actualf' standard deviations for MW measurements are slightly higher than the above values but much lower than the 1.29% of FSR derived from the specified precisions for instruments in the measurement chain.

DISCUSSION

The experience with the 500/230kV Transmission Station and a number of other substations has shown that:

1- In general, sufficient measurement redundancies are monitored at the control center for each substation to provide a set of over determined equations whose minimization could yield calibration coefficients for reducing the systematic errors and estimating the prevailing standard deviations.

2- The procedure presented here provides satisfactory results for typical variation of gains and zero offsets, which are between 100f2.5%, and +2.5%, respectively. The larger variations usually indicate defective or out-of- range instruments needing field inspections.

3- The systematic errors are about an order of magnitude greater than the random errors. However, they vary in a recognizable pattern over the range of measurements and can be identified and minimized.

4- The random errors have normal distribution. Their actual and prevailing standard deviations can be estimated remotely. Their values are about an order of magnitude lower than the standard deviations derived from the specified precision of instruments in the measurement streams.

CONCLUSION

The on-line computer applications such as monitoring of power system security require an accurate real-time data-base which is to be provided by state estimators. The convergence and behavior of the state estimators in turn depend on the accuracy of analog measurements. Therefore, it is important that the uncertainties in analog measurements be estimated and reduced to a level that allows greater confidence in the results of the state estimators and the related applications.

State estimators require zero-mean analog measurements and actual standard deviations for rapid convergence and minimum residuals. This paper has shown a procedure for reducing the systematic errors and estimating the prevailing standard deviations.

By relieving the state estimators from the tasks of detecting, identifying and eliminating the installation errors and systematic errors in measurements, and by providing the actual and prevailing stapdard deviations of measurements, the state estimator can detect, identify and suppress

908

the intermittent errors caused by the communication and furnish a more reliable real-time data-base for the computer control of power systems.

The integration of the methodology described in this paper with state estimation provides a more reliable real-time data-base and therefore, more dependable on-line security applications.

REFERENCES

M. M. Adibi and D. K. Thorne, "Remote Measurement Calibration, IEEE Trans. on Power Systems, Vol. PWRS-l,No.2/, pp. 194-203, May 1986.

M. M. Adibi and J. P. Stovall, "On Estimation of Uncertainties in Analog Measurements,lV IEEE PES 89 SM 669-3-PWRS, 1989.

Edison Electric Institute , IIHandbook f o r Electricity Metering," Eighth Edition, 1981, pp.223-245

E. H. Povy, ttAccuracy Tests on Installed Capacitance-Coupled Potential Devices,"

M. Merrill and F. C. Schweppe, "Bad Data Suppression in Power System Static State Estimator,I1 IEEE Trans.PAS-90, pp. 2718- 2725, 1971.

J. R. Taylor, "An Introduction to Error Analysis," Denver, University Science Books, 1982, pp. 56-73.

R. Fletcher and M. J. D. Powell, "A Rapid Descent Method of Minimization," The Com- puter Journal, Vo1.6(2),pp.163-168, 1963.

IEEE PES 74 SM C74-375-2, 1974.

ACKNOWLEDGEMENT

The first author wishes to express his appreciation to Hydro-Quebec, Potomac Electric Power Company, and Southern Company Services, Inc., for supporting the development of the "Remote Measurement Calibration" program.

BIOGRAPHY

M. M. Adibi (M'56, SM'70) received the B.Sc. degree with honors in electrical engineering from the University of Birmingham, England,in June 1950, and the M.E.E. degree from Polytechnic Institute of Brooklyn in January, 1960. Since 1950, he has assumed various responsibilities in the electric utility industry; about one half of which has been at IBM Corp. He is at the present a consultant with IRD Corp., engaged in power system computer applications.

Mr, Adibi is the author of over thirty IEEE papers, a member of Power System Engineering Committee, Chairman of Power System Restoration Task Force, Chartered Electrical Engineer, UK, and a Professional Engineer in the State of Maryland.

R. J. Kafka (Mr73,SMt88) received the B.S.E.P. degree from Regis College in Denver in 1970, and the MS degree from Purdue University in 1972. Since 1973, he has been employed by the Potomac E1ectri.c Power Company assuming various engineerlng responsibilities related to substations, generation control, and system analysis. At the present he is Manager, Power Pooling Economics.

Mr. Kafka is a member of Power System Restoration Task Force, Power Engineering Society, Computer Society and is a Registered Professional Engineer in the State of Maryland.

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Discussion estimator’s input database and in turn lead to a better overall llreal-timelt estimate of the state of a power system. The following issues require L. Mili and vs Phanimj, polytechnic Institute and state

University, Blacksburg,): The authors should be commended for their interesting paper d&g with the remote measurement calibration. Mea- surement calibration is a prerequisite to the state estimation function since bad data identification can be achieved only if the majority of the measurements are valid. Indeed, the maximum fraction that any robust estimator can deal with is equal to half of the redundant measurements, [(m - n)/2]; here m is the number of measurements and n is the number of variables to be estimated.

We agree with the principle of the method proposed by the authors. However, some comments are in order:

1) Remote calibration should be performed only when there are enough redundancy in the measurements; this requirement i s imposed by the fact the state variables are not constant but change from one estimation to the other.

2) The least squares estimator suggested for estimating the calibration coefficients (off-sets and gains) is not robust against bad measure- ments; its bias may be carried over all bounds by the action of a single gross error. Robust estimators should be used instead. In the absence of leverage points, i.e. when the data points are evenly distributed in the ( I , , I , , 13, - * a , 16) space, where

M-estimators such as the Menill-Schweppe estimator [5] or the Least Absolute Value estimator [A] can be used. Both methods are able to withstand a fraction of contamination up to 25 46 and may be implemented through fast algorithms. However, when the multiple regression possesses leverage points, then high breakdown estimators are needed. One of them, namely the least median of squares estimator, has been recently applied to power systems p, C]. Note that the leverage points are data points which are distant from the bulk of the point cloud in the ( 1, , 12,

3) The average (AVG) and the root mean square (RMS) are good estimates only under the Gaussian assumption. However, as pin- pointed by the authors, the measurement errors result from the combination of small noise, systematic errors and intermittent errors, whose probability distributions are likely to be longer tailed and asymmetric. As a result, the AVG and the RMS as an estimate of the center and of the scale (dispersion) of the distribution are biased. Here, we should use the median instead of the AVG and the median absolute deviation (MAD) instead of the RMS. The MAD is defined

a , f6) space.

as

MAD=1.4826 med (Izi-medzjl) I I

where zi are the random quantities under study.

References

[A] M. R. Irving, R. C. Owen and M. Sterling, “Power System State Estimation using Linear Programming,” Proceedings of the ZEE, Vol. 125, No. 9, Sept. 1978, pp. 879-885.

p ] L. Mili, V. Phaniraj and P. J. Rousseeuw, “High Breakdown Point Estimation in Electric Power Systems,” Proceedings of the 1990 Znternationaf Symposium on Circuit and Systems, New Orleans, May 8-11, 1990.

[C] L. Mili, V. Phaniraj and P. J. Rousseeuw, “Robust Estimation Theory for Bad Data Diagnostics in Electric Power Systems,” in Advances in Control and Systems, C. T. Leondes (ed.), Academic Press, Vol. XXXVI, under press.

Manuscript received March 2,1990

W. 0. STADLIN (Macro Corp., Horsham, PA): There is wide agreement that the input to a power system state estimator should be as error free and simultaneous as is practical to achieve. This includes the power system model as well as analog and status information. The paper demonstrates an “off -linert procedure that can be expected to improve a state

The transformer model appears to be based on known transformation ratio between the ltequivalenttt primary and secondary current magnitudes. What is the impact of this assumption, considering the effects of exciting current (magnetizing and losses) and saturation? How should uncertainties in fixed and telemetered tap position be taken into account? Can the authors’ methods be extended to multi-winding transformers?

The calibration procedure appears to be a two- step process. Step 1 - 500 kV lines and transformer secondary. Step 2 - 230 kV lines. Would there be any significant improvement if these two steps were combined in order to obtain a joint calibration of all the measurements?

The measurement set appears to require some screening. What checks need to be applied to ensure that there is sufficient data for error analysis and that the data spans a wide enough range to be to able to calculate a unique set of calibration coefficients?

L. MIL1 and V. PHANIRAJ (Virginia Polytechnic Institute, Blacksburg, VA): The authors should be commended for their interesting paper with the remote measurement calibration. Measurement calibration is a prerequisite to the state estimation function since bad data identification can be achieved only if the majority of the measurements are valid. Indeed, the maximum fraction that any robust estimator can deal with is equal to half of the redundant measurements, [(m-n)/2]; here m is the number of measurements and n is the number of variables to be estimated.

We agree with the principle of the method proposed by the authors. However, some comments are in order:

1) Remote calibration should be performed only when there are enough redundancy in the measurements: this requirement is imposed by the fact the state variables are not constant but change from one estimation to the other.

2) The least squares estimator suggested for estimating the calibration coefficients (off- sets and gains) is not robust against bad measurements; its bias may be carried over all bounds by the action of a single gross error. Robust estimators should be used. instead. In the absence of leverage points, i.e. when the data points are evenly distributed in the (11, 12, 13,...,16) space, where

11 = Vt, 13 = Ptr 15 = Qt, l3 = Vt2, l4 = Pt2, 16 = Qt2.

M-estimators such as the Merrill-Schweppe estimator [5] or the Least Absolute Value estimator [A] can be used. Both methods are able to withstand a fraction of contamination up to 25 % and may be implemented through fast algorithms. However, when the multiple regression possesses leverage points, then high breakdown estimators are needed. One of them, namely the least median of square

910

estimator , has been recently applied to power systems [B,C]. Note that the leverage points are data points which are distant from the bulk of the point cloud in the (l~,l~,..,,l~) space.

3 ) The average (AVG) and the root mean square (RMS) are good estimates only under Gaussian assumption. However, as pinpointed by the authors, the measurement errurs result from the combination of small noise, systematic errors and intermittent errors, whose probability distributions are likely to be >. As a result, the AVG and the RMS as an estimate of the center and of the scale (dispersion) of the distribution are biased. Here, we should use the median instead of the AVG and the median absolute deviation (MAD) instead of RMS. The MAD is defined as

MAD = 1.4826 med ( I z ~ - med Zi() 3

where zi are the random quantities under study.

References:

[A] M.R. Irving, R.C. Owen and M. Sterling, "Power System State Estimation Using Linear Programming, "Proceeding of the IEE , Vol. 125 , No. 9, Sept. 1978, pp. 879-885.

[B] L. Mili, V. Phaniraj and P.J. Rousseeuw, "High Breakpoint Estimation in Electric Power Systems,I* Proceeding of 1990 International Symposium on circuit and Systems, New Orleans, May 8-11, 1990.

[C] L. Mili, V. Phaniraj and P.J. Rousseeuw, 'IRobust Estimation Theory for Bad Data Diagnostics in Electric Power Systems , in Advances in Control Systems, C.T. Leondes (ed), Academic Press, Vol.XXXV1, under press.

H. M. ADIBI and R. J. KAFKA: The authors thank the discussers for their comments and questions, which allow clarification of some points in the paper.

Responding to W . Stadlin's questions:

1. In the Ampere Equality equation (2), the transformer's excitation current is well within the random errors of the transformer currents (which are derived from the V, P & Q measurements), and therefore it can be ignored in the calibration proceeding. Thus the transformer model used is the same as those used in typical network analysis where the series resistance and reactance are represented but the shunt values are ignored. The 500/230 kV transformer considered has off- nominal ratio and tap changer, both of these values were known during the 96 "hourlyff data collections and were considered by the ratio Q in the equation (2). In order to extend the

calibration method to transformer tap positions and network parameters the authors intend to consider connecting lines to the adjacent stations. It is our experience that in general sufficient measurements are monitored at the control centers to allow representation and calibration of multi- winding transformers.

2. In the remote measurement calibration of the station reported in [ 11 , there were ample measurement redundancies available to allow the simultaneous minimizatidn of MVA Equality and BUS Summing (for P & Q) and Voltage Equality. The results did not compare favorably with the results of minimizations in two steps. We agree with Mr. Stadlin that this is an area worthy of further investigation.

3. The data rejection routine screens unreasonable input data and the measurement classification routine checks that adequate number (samples) and sufficient range of measurements are available before entering the minimization routine.

In response to questions and comments by Dr. Mili and Dr. Phaniraj :

1. The state estimator uses telemetered voltage, real and reactive powers at an tlinstantfl in time and provides state variables which change with time. The remote measurement calibration method described in this paper uses the same telemetered values, but over a period of several days, evaluating the random errors and minimizing the systematic errors in the measurements. The standard deviations evaluated changes with replacement of the defective instruments in the measurement stream. The calibration coefficients ( i.e., offsets, gains and nonlinearities) obtained may gradually change due to drift and deterioration of instruments. However, these changes do not occur over short period such as from one estimation to the other.

2. The authors have had no experience with M- estimation nor with Absolute Value estimator, but are aware of effects of the leverage points. By properly selecting the input data, they are evenly distributed over the measurement range between the low and the high readings thus avoiding the leverage points.

3 . The "averagefg used in equation (8), and the llroot mean squaret' used in measurement classification [l], are based on normal di'stributions. These two estimates give reasonably accurate results even when the normality assumption is approximately satisfied. The comparison of the average with the median and the root mean square with the median absolute deviation in this application have shown no significant differences. This may well be due to the data preparation, data rejection and result classification subroutines of the RMC program.